Abstract

Using molecular dynamics simulations and the capillary fluctuation method, we have calculated the anisotropic crystal-melt interfacial free energy and stiffness of aluminum in a rapid solidification system where a temperature gradient is applied to enforce thermal non-equilibrium. To calculate these material properties, the standard capillary fluctuation method typically used for systems in equilibrium has been modified to incorporate a second-order Taylor expansion of the interfacial free energy term. The result is a robust method for calculating interfacial energy, stiffness and anisotropy as a function of temperature gradient using the fluctuations in the defined interface height. This work includes the calculation of interface characteristics for temperature gradients ranging from 11 to 34 K/nm. The captured results are compared to a thermal equilibrium case using the same model and simulation technique with a zero gradient definition. We define the temperature gradient as the change in temperature over height perpendicular to the crystal-melt interface. The gradients are applied in MD simulations using defined thermostat regions on a stable solid-liquid interface initially in thermal equilibrium. The results of this work show that the interfacial stiffness and free energy for aluminum are dependent on the magnitude of the temperature gradient, however the anisotropic parameters remainmore » independent of the non-equilibrium conditions applied in this analysis. As a result, the relationships of the interfacial free energy/stiffness are determined to be linearly related to the thermal gradient, and can be interpolated to find material characteristics at additional temperature gradients.« less

@article{osti_1344368,
title = {Interfacial free energy and stiffness of aluminum during rapid solidification},
author = {Brown, Nicholas T. and Martinez, Enrique and Qu, Jianmin},
abstractNote = {Using molecular dynamics simulations and the capillary fluctuation method, we have calculated the anisotropic crystal-melt interfacial free energy and stiffness of aluminum in a rapid solidification system where a temperature gradient is applied to enforce thermal non-equilibrium. To calculate these material properties, the standard capillary fluctuation method typically used for systems in equilibrium has been modified to incorporate a second-order Taylor expansion of the interfacial free energy term. The result is a robust method for calculating interfacial energy, stiffness and anisotropy as a function of temperature gradient using the fluctuations in the defined interface height. This work includes the calculation of interface characteristics for temperature gradients ranging from 11 to 34 K/nm. The captured results are compared to a thermal equilibrium case using the same model and simulation technique with a zero gradient definition. We define the temperature gradient as the change in temperature over height perpendicular to the crystal-melt interface. The gradients are applied in MD simulations using defined thermostat regions on a stable solid-liquid interface initially in thermal equilibrium. The results of this work show that the interfacial stiffness and free energy for aluminum are dependent on the magnitude of the temperature gradient, however the anisotropic parameters remain independent of the non-equilibrium conditions applied in this analysis. As a result, the relationships of the interfacial free energy/stiffness are determined to be linearly related to the thermal gradient, and can be interpolated to find material characteristics at additional temperature gradients.},
doi = {10.1016/j.actamat.2017.02.033},
journal = {Acta Materialia},
number = C,
volume = 129,
place = {United States},
year = {2017},
month = {5}
}

This project focused on thermoelectric transport in semiconductor micro and nanostructures where moderate and typical operating voltages and currents lead to extreme thermal gradients and current densities. Models that describe behavior of semiconducting materials typically assume an equilibrium condition or slight deviations from it. In these cases the generation-recombination processes are assumed to have reached a local equilibrium for a given temperature. Hence, free carrier concentrations and their mobilities, band-gap, thermal conductivity, thermoelectric properties, mobility of atoms and mechanical properties of the material, can be described as a function of temperature. In the case of PN junctions under electrical bias,more » carrier concentrations can change up to ~ 1020 cm-3 and a drift-diffusion approximation is typically used to obtain the carrier concentrations while assuming that the material properties do not change. In non-equilibrium conditions, the assumption that the material properties remain the same may not be valid. While the increased conduction-band electron concentration may not have a drastic effect on the material, large hole concentration is expected to soften the material as ‘a hole’ comes into existence as a broken bond in the lattice. As the hole density approaches 1022 cm-3, the number of bonds holding the lattice together is significantly reduced, making it easier to break additional bonds, reduce band-gap and inhibit phonon transport. As these holes move away from where they were generated, local properties are expected to deviate significantly from the equilibrium case. Hence, temperature alone is not sufficient to describe the behavior of the material. The behavior of the solid material close to a molten region (liquid-solid interfaces) is also expected to deviate from the equilibrium case as a function of hole injection rate, which can be drastically increased or decreased in the presence of an electric field. In the past years we have investigated the possible thermoelectric explanation of asymmetric melting of self-heated Si micro-structures using equilibrium materials’ properties that exist in the literature. We have analyzed the contribution of the electrons and the holes and identified the generation-transport-recombination of minority carriers (GTR) as the reason for an extreme change in the thermal profile in presence of strong generation and electric field. A more complete analysis required construction of models that capture the individual generation and recombination processes to understand the thermal profile as well as the possibility of electronic softening and non-equilibrium melting of the structure below melting temperature. The possibility of melting a material at a lower temperature breaks the correlation between the atomic mobility and the kinetic energy in the system for a given temperature and may allow alternative growth processes. This may also be the mechanism behind ‘amorphization-without-melting in layered structures heated with laser pulses’ that has been reported earlier. The conventional models for semiconductors are constructed for low temperature operation and their projections to higher temperatures do not yield reasonable carrier concentrations. Using these models, the free hole concentrations are calculated to be on the order of 1019 cm-3 at melting, which also do not correlate well with the latent heat of fusion. The melt is expected to correspond to broken bond concentrations on the order of the atomic density (~5x1022 cm-3 for Silicon). Hence, using conventional models the thermoelectric contribution expected from the GTR process is estimated to be much smaller than it likely is. Our work focused on improving the computational models and electrical characterization of materials and devices to better understand thermoelectric trabsport under extremen thermal gradients and current densities. Specifically, during this project, we have - Expanded our computational models to include self-consistent solution of Poisson charge equation (together with current and heat equations currently solved) for improved accuracy of role of bipolar conduction, - Developed a crystallization model incorporating experimentally determined nucleation rates and growth velocities to enable simulation of grain growth, growth-from-melt, filament formation and retention, - Performed high-temperature characterization of relevant materials (including metal contacts, interfacial and insulation layers); electrical and thermal conductivities, Seebeck coefficient, carrier mobility and concentration, - Performed High-speed device-level characterization of metastable amorphous and crystalline phases, crystallization and amorphization dynamics, melting and crystalline growth-from-melt, - Observed and characterized formation of microplasmas in electrically stressed ZnO nanoforests.« less

This first CMSN project has been operating since the summer of 1999. The main achievement of the project was to bring together a community of materials scientists, physicists and mathematicians who share a common interest in the properties of interfaces and the impact of those properties on microstructural evolution. Six full workshops were held at Carnegie Mellon (CMU), Northwestern (NWU), Santa Fe, Northeastern University (NEU), National Institute for Standards and Technology (NIST), Ames Laboratory, and at the University of California in San Diego (UCSD) respectively. Substantial scientific results were obtained through the sustained contact between the members of the project.more » A recent issue of Interface Science (volume 10, issue 2/3, July 2002) was dedicated to the output of the project. The results include: the development of methods for extracting anisotropic boundary energy and mobility from molecular dynamics simulations of solid/liquid interfaces in nickel; the extraction of anisotropic energies and mobilities in aluminum from similar MD simulations; the application of parallel computation to the calculation of interfacial properties; the development of a method to extract interfacial properties from the fluctuations in interface position through consideration of interfacial stiffness; the use of anisotropic interface properties in studies of abnormal grain growth; the discovery of abnormal grain growth from random distributions of orientation in subgrain networks; the direct comparison at the scale of individual grains between experimentally observed grain growth and simulations, which confirmed the importance of including anisotropic interfacial properties in the simulations; the classification of a rich variety of dendritic morphologies based on slight variations in the anisotropy of the solid-liquid interface; development of phase field methods that permit both solidification and grain growth to be simulated within the same framework.« less

Both academia and industry alike have paid close attention to the mechanisms of microstructural selection during the solidification process. The forces that give rise to and the principles which rule the natural selection of particular morphologies are important to understanding and controlling new microstructures. Interfacial properties play a very crucial role to the selection of such microstructure formation. In the solidification of a metallic alloy, the solid-liquid interface is highly mobile and responds to very minute changes in the local conditions. At this interface, the driving force must be large enough to drive solute diffusion, maintain local curvature, and overcomemore » the kinetic barrier to move the interface. Therefore, the anisotropy of interfacial free energy with respect to crystallographic orientation is has a significant influence on the solidification of metallic systems. Although it is generally accepted that the solid-liquid interfacial free energy and its associated anisotropy are highly important to the overall selection of morphology, the confident measurement of these particular quantities remains a challenge, and reported values are scarce. Methods for measurement of the interfacial free energy include nucleation experiments and grain boundary groove experiments. The predominant method used to determine anisotropy of interfacial energy has been equilibrium shape measurement. There have been numerous investigations involving grain boundaries at a solid-liquid interface. These studies indicated the GBG could be used to describe various interfacial energy values, which affect solidification. Early studies allowed for an estimate of interfacial energy with respect to the GBG energy, and finally absolute interfacial energy in a constant thermal gradient. These studies however, did not account for the anisotropic nature of the material at the GBG. Since interfacial energy is normally dependent on orientation of the crystallographic plane of the solid with respect to the liquid, a better calculation of interfacial energy was needed. Herring described this orientation dependence, which related the interfacial undercooling to the principle interfacial curvatures. The present study pertains to the measurement of the anisotropy of interfacial energy by comparison of experimental and theoretical GBG geometries in pure succinonitrile (SCN) and pivalic acid (PVA). A quantity of SCN and PVA was distilled and zone refined using a process that is defined in the experimental procedure portion of this paper. Very thin (100 {micro}m) slide assemblies were created and filled with these organic materials. For each system, several grooves were photographed and their shapes were compared with theoretical predictions. The correlation between experiment and theory was quantified and plotted as a function of the anisotropy for each of the GBG's examined, and a maximum correlation corresponded to the anisotropy of interfacial energy which describes that particular rotation of the GBG. The results from several rotations were statistically analyzed to ensure confidence in the measurement of the anisotropy of interfacial energy and, finally, compared to reported values obtained with other techniques.« less

The summary below is an update of our previous progress report of June, 2003. That previous progress report, which was submitted as a PDF document, is not recorded on the RIMS website but will appear on the EMSP website. Our recent results are in the following areas: (1) Single-component flow through a rough-walled fracture to validate our methods, we have simulated slow single-component fluid flow through a geometry taken from analogous laboratory experiments. The permeability of this fracture is studied as the direction of the driving force is changed. We find that the lattice-Boltzmann method agrees with the experimental datamore » and with previous numerical efforts. Additionally, flow enhancement compared to the well-known cubic law is observed in certain directions, i.e., the direction in which channels are most strongly correlated. Conversely, flow inhibition is observed in the perpendicular direction. Fluid flow appears to follow the correlated channels. We are currently extending these studies to higher Reynolds numbers where classical approximations based on assumptions of slow creeping flow are no longer valid. (2) Capillary rise in simple and complex geometries Capillary rise is studied using the lattice-Boltzmann method. The geometries used are a circular tube, a rectangular tube, and a fracture between two rough walls. The capillary rise height and the shape of the interface is studied as a function of the size of the tube, the wetting tendency of the walls, the surface tension, and the magnitude of an applied body force. In performing this study we discovered a technical problem with the lattice-Boltzmann method: it exhibited lattice pinning. This pinning created two significant problems: the entrapment of small bubbles and a history dependence of the contact angle. We solved these problems by modifying our algorithm so that it now allows interfaces to move at a smaller velocity. The new method practically removes all effects of lattice pinning. For the case of rectangular tubes, we have shown that the shape of the interface follows theoretical predictions and that the pressure drop across the interface obeys Laplace's law. Consequently our improved method solves a significant problem encountered in lattice-Boltzmann simulations of drainage and imbibition. We are presently pursuing analogous studies in more complex geometries. (3) Macroscopic laws for two-component fluid flow through rough fractures. Macroscopic two-phase flow through porous media is commonly approximated by a generalization of Darcy's law, wherein ''relative permeability's'' represent the mobility of wetting and non-wetting fluids. We have recently begun studying the applicability of this approximation for two-phase flow through rough-walled fractures. We find that when the nonwetting fluid is unconnected it can become trapped in tight geometries. Once forcing exceeds a certain capillary threshold the non-wetting fluid starts to move again. This capillary threshold depends on the roughness of the fracture surface and the size of the fracture aperture. Further simulations are being performed to better specify these dependencies along with the relationship of relative permeability to fracture roughness. (4) Multiple relaxation-time lattice-Boltzmann method. We are exploring ways to use the lattice-Boltzmann method in a rectangular lattice with different spacing in one direction. This idea is motivated by the fact that self-affine fracture surfaces exhibit different scaling perpendicular to the plane of the fracture than they exhibit in the plane. Therefore, allowing different lattice spacing in the different directions should greatly increase the efficiency of our simulations. We also seek a practical way of solving a well-known problem that derives from using the ''bounce-back'' method to approximate no-slip boundary conditions. We are pursuing a new generalization of the ''multiple relaxation time generalized lattice-Boltzmann method'' and are in the process of implementing it. (5) Study of thermal fluctuations of fluid-fluid interfaces. We have included thermal fluctuations in our model. These fluctuations lead to a roughening of fluid-fluid interfaces. We have demonstrated that the roughening follows theoretical predictions. We are presently pursuing applications to the study of the formation and growth of capillary bridges in rough fractures.« less

A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized whichmore » determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing generally occurs before the liquid length is reached. As a result, the significance of the presented modeling expressions is established by a direct comparison to a reduced model, which utilizes widely applied approximations but fundamentally fails to capture the physical complexity discussed in this paper.« less